Answer:
56 + 40
Step-by-step explanation:
multiply what is in the parenthesis, don't solve all the way because the instructions say to simplify.
If y=cosh(4tanh¯¹x) then dy/dx=
If you're like me and don't remember hyperbolic identities (especially involving inverse functions) off the top of your head, recall the definitions of the hyperbolic cosine and sine:
[tex]\cosh(x) = \dfrac{e^x + e^{-x}}2 \\\\ \sinh(x) = \dfrac{e^x - e^{-x}}2[/tex]
Then differentiating yields
[tex]\dfrac{\mathrm d(\cosh(x))}{\mathrm dx} = \dfrac{e^x-e^{-x}}2 = \sinh(x) \\\\ \dfrac{\mathrm d(\sinh(x))}{\mathrm dx} = \dfrac{e^x+e^{-x}}2 = \cosh(x)[/tex]
so that by the chain rule, if
[tex]y = \cosh\left(4\tanh^{-1}(x)\right)[/tex]
then
[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{\mathrm d\left(\cosh\left(4\tanh^{-1}(x)\right)\right)}{\mathrm dx} = \sinh\left(4\tanh^{-1}(x)\right) \dfrac{\mathrm d\left(4\tanh^{-1}(x)\right)}{\mathrm dx}[/tex]
Now, let [tex]z=4\tanh^{-1}(x)[/tex], so that (•) [tex]\tanh\left(\frac z4\right) = x[/tex].
Recall that
[tex]\tanh(x) = \dfrac{\sinh(x)}{\cosh(x)} = \dfrac{e^x-e^{-x}}{e^x+e^{-x}}[/tex]
and so the derivative of tanh(x) is
[tex]\dfrac{\mathrm d(\tanh(x))}{\mathrm dx} = \dfrac{(e^x+e^{-x})(e^x+e^{-x})-(e^x-e^{-x})(e^x-e^{-x})}{(e^x+e^{-x})^2} \\\\ = \dfrac{4\cosh^2(x)-4\sinh^2(x)}{4\cosh^2(x)} \\\\ = 1-\tanh^2(x) = \mathrm{sech}^2(x)[/tex]
where the last equality follows from the hyperbolic Pythagorean identity,
[tex]\cosh^2(x)-\sinh^2(x) = 1 \implies 1-\tanh^2(x) = \mathrm{sech}^2(x)[/tex]
Differentiating both sides of (•) implicitly with respect to x gives
[tex]\dfrac{\mathrm d\left(\tanh\left(\frac z4\right)\right)}{\mathrm dx} = \dfrac{\mathrm d(x)}{\mathrm dx} \\\\ \mathrm{sech}^2\left(\dfrac z4\right)\dfrac{\mathrm d\left(\frac z4\right)}{\mathrm dx} = 1 \\\\ \dfrac14 \mathrm{sech}^2\left(\dfrac z4\right) \dfrac{\mathrm dz}{\mathrm dx} = 1 \\\\ \dfrac{\mathrm dz}{\mathrm dx} = 4\cosh^2\left(\dfrac z4\right) \\\\ \dfrac{\mathrm dz}{\mathrm dx} = 4\cosh^2\left(\tanh^{-1}(x)\right)[/tex]
So, the derivative we want is the somewhat messy expression
[tex]\boxed{\dfrac{\mathrm dy}{\mathrm dx} = 4\sinh\left(4\tanh^{-1}(x)\right) \cosh^2\left(\tanh^{-1}(x)\right)}[/tex]
and while this could be simplified into a rational expression of x, I would argue for leaving the solution in this form considering how y is given in this form from the start.
In case you are interested, we have
[tex]\cosh\left(\tanh^{-1}(x)\right) = \dfrac1{\sqrt{1-x^2}}[/tex]
and you can instead work on differentiating that; you would end up with
[tex]\dfrac{\mathrm dy}{\mathrm dx} = -\dfrac{16x^3+16x}{(x^2-1)^3}[/tex]
YALL PLSSSSSSSS HELP IM SHAKING I NEED HELP PLSS
Answer:
someone is adding dont worrie
Step-by-step explanation:
Which of the functions below could have created this graph?
Answer:
D.
Step-by-step explanation:
End behavior : Left up and right down
Even degree with negative leading coefficient
Evaluate -c when c = 12
Answer: [tex]-12[/tex]
Step-by-step explanation:
[tex]-c=-(12)=\boxed{-12}[/tex]
Two numbers that will multiply to -21 and also add to 4
Answer:
the numbers are 7 and -3
Step-by-step explanation:
Answer:
7 and -3 are the numbers
Step-by-step explanation:
7-3= 4
7×-3= -21
¿Cuántas combinaciones se pueden
hacer con una letra del abecedario
(tiene 27 letras diferentes) y los números
8 y 14?
Queremos ver cuantas combinaciones diferentes se pueden hacer con una letra del abecedario y los números 8 y 14.
La respuesta es:
Hay 162 combinaciones diferentes.
Primero dejemos la letra fija, asumamos que queremos ver las combinaciones entre la letra A, el número 8, y el número 14.
Tenemos 3 elementos, entonces el número de combinaciones será solo 3 factorial, o:
combinaciones = 3! = 3*2*1 = 6
Hay 6 combinaciones diferentes de esos 3 elementos.
Ahora recordamos que ademas de A hay 26 opciones más, entonces la letra tiene un total de 27 permutaciones posibles. Es decir, el número total de combinaciones va a ser 27 veces lo que obtuvimos arriba:
Total de combinaciones = 6*27 = 162
Hay 162 combinaciones diferentes.
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Write a problem based on the given information.
7.) c = cost per pound of plain coffee beans
C + 3 = cost per pound of flavored coffee
beans 2c + (c + 3) = 21
A jar contains 2000 marbles. If 61.5% of them are red, 27.5% are white, and 10% of them are blue, how many marbles are neither red, white, or blue?
Answer:
1 percent, or 20 marbles
Step-by-step explanation:
add all the other percentages and it sums up to 99%. and the other one percent of the marbles is 20.
Answer:
20 marbles
Step-by-step explanation:
61.5 + 27.5 + 10 = 99
this means 1% are neither red, white or blue
1% of 2000 is 20
HELPPPPPPP FASSSSSSSSST THIS IS DUE
Nolan’s car used 2 gallons to travel 50 miles. How far can he travel on 3 gallons?
Answer:
75 miles
Step-by-step explanation:
because half of 50 is 25 so 25x2 is 50 and 50 plus 25 is 75
Answer:
75
Step-by-step explanation:
count by 25's
25+25=50
50+25=75
show work and ill mark brainliest :)
Answer:
parallel
Step-by-step explanation:
AB
m= 19-(-9)/8-(-6)
m=28/14
m=2
CD
m=0-(-4)/2-0
m=4/2
m=2
parallel:m1=m2
perpendicular:m1m2= -1
therefore its parallelA snail is at the bottom of a 10 foot well. Every
day, he crawls up 3 feet, but at night, he slips
down 2 feet. How many days will it take for him to get
out of the well?
Answer:
10 days.
Step-by-step explanation:
3-2 = 1 foot of progress per day.
Answer:
8 days
Step-by-step explanation:
We get 8 days because the snail gets one foot higher every day. By the morning of the 8th day, the snail is 7 feet up and just needs to climb its daily 3 feet and it will be out of the well. You don't need 10 days because the snail only falls at night.
102÷6 what is the Anser
Answer:
17 good luck
Step-by-step explanation:
the answer is 17
102/6= 17
Answer:
17
Step-by-step explanation:
it just is
hope this helps, I am writing because I need words
simplify -4/3 / 2/-6
Answer: 4
Step-by-step explanation:
Multiply by reciprocal of 2nd term, and simplify
-4/3 / 2/-6 = -4/3 * -6/2 = -4/3 * -3 = 4
-4 * -2 = 8
3 * -2 = -6
so, now we have
8/-6 ÷ 2/-6
8/-6 × -6/2
-48/-12
4
Ahmed bought 5 equally priced markers for $3.25.
How much will 12 of these markers cost?
$1.35
$6.68
$7.80
$8.46
Answer:
$7.80
Step-by-step explanation:
Find the unit price by dividing 3.25 by 5.
3.25 ÷ 5 = 0.65
Now that you have the unit price, multiply it by 12 to find the total price of the 12 markers.
0.65 × 12 = 7.80
Thus, 12 of the same markers that Ahmed bought will cost $7.80.
The cost of 12 markers is given by the equation A = $ 7.80
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the number of markers be n = 5
The cost of 5 markers = $ 3.25
So , the cost of 1 marker = cost of 5 markers / 5
On simplifying the equation , we get
The cost of 1 marker = 3.25 / 5
The cost of 1 marker = $ 0.65
Now , the cost of 12 markers = 12 x cost of 1 marker
Substituting the values in the equation , we get
The cost of 12 markers A = 12 x $ 0.65
The cost of 12 markers A = $ 7.80
Hence , the equation is A = $ 7.80 , where A is the total cost of markers
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El diseño de un sistema requiere instalación de 2 componentes iguales. El sistema completo funcionará si al menos 1 de los componentes funcionan,mientras que un sistema alternativo requiere cuatro de sus componentes funcionará si al menos 2 de sus componentes están funcionando.
La probabilidad de que un componente funcione de manera individual es de 0.9 y cada uno funciona de manera independiente. ¿cuál de los 2 diseños tienen mayor probabilidad de funcionar?
Usando la distribución binomial, se encuentra que el diseño de 4 componentes tiene mayor probabilidad de funcionar.
Para cada componente, solo hay dos resultados posibles. O están funcionando o no estan. La probabilidad de que un compoente estea funcionando es independiente de cualquier otro componente, lo que significa que se utiliza la distribución binomial para resolver esta cuestión.
Distribuición binomial:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Los parámetros son:
n es el número de ensayos. p es la probabilidad de éxito en un ensayo. x es el número de éxitos.En este problema:
La probabilidad que un componente funcione es 0.9, o sea, [tex]p = 0.9[/tex].Diseño de 2 componentes:
2 componentes implica que [tex]n = 2[/tex].La probabilidad de funcionar es [tex]P(X \geq 1)[/tex], que es dada por:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
En que:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.9)^{0}.(0.1)^{2} = 0.01[/tex]
Entonces:
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.01 = 0.99[/tex]
Diseño de 4 componentes:
4 componentes implica que [tex]n = 4[/tex].La probabilidad de funcionar es [tex]P(X \geq 2)[/tex], que es dada por:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
En que:
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{4,0}.(0.9)^{0}.(0.1)^{4} = 0.0001[/tex]
[tex]P(X = 1) = C_{4,1}.(0.9)^{1}.(0.1)^{3} = 0.0036[/tex]
Entonces:
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0001 + 0.0036 = 0.0037[/tex]
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.0037 = 0.9963[/tex]
[tex]0.9963 > 0.99[/tex], o sea, el diseño de 4 componentes tiene mayor probabilidad de funcionar.
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Explain how you can use doubles when
multiplying with 4 to find 4 X 8.
Multiplying by 4 using the doubles strategy utilizes the fact that 4 is double of 2. Hence, 4 time any number is double of 2 times that number. Thus, given 4 x 8, it can be evaluated using the double strategy as follows 2 x 8 + 2 x 8 = 16 + 16 = 32
Y=arccos(1/x)
Please help me do them all! I don’t know derivatives :(
Answer:
Step-by-step explanation:
Somone help me plzzzz
Answer:
There are 8 flowers.
Step-by-step explanation:
You have the 3 you filled in correct. Since there are 12 flowers, and we know that there are only two colors, once we know one color we can figure the other one out. We are told that there are 4 pink flowers. Since we know there are 4 pink flowers, we can do subtraction to find how many red flowers there are. 12-8=4. You begin with 12, then count back 4. 11, 10, 9, and then 8. This is how you find the answer. I hope this helps!
MULTIPLE CHOICE QUESTION
What is the highest degree of a polynomial
that can be used as a divisor in synthetic
division?
Explanation:
Polynomials of degree 1, aka linear polynomials, are the highest allowed for the divisor when using synthetic division. If the divisor is degree 2 and larger, then you'll need to use polynomial long division instead.
An example divisor of degree 1 is something like [tex]x+5[/tex], which can be written as [tex]x^1+5[/tex]. That exponent of 1 determines the degree.
How many solutions are there for this equation? Why?
Answer:
d
Step-by-step explanation:
Factor 10xy-25x-16y+40=
(2y−5)(5x−8)
step by step Explanation:
10xy−25x−16y+40
10xy−25x−16y+40
=(2y−5)(5x−8)
hope it helps
You would like to start a club for psychology majors on campus, and you are interested to find out what proportion of psychology majors would join. The dues would be $35 and used to pay for speakers to come to campus. You ask five psychology majors from your senior psychology honors seminar whether they would be interested in joining this club and find that four of the five students questioned are interested. Is this sampling method biased, and if so, what is the likely direction of bias
From the sample used to find out what psychology majors would join the club and if it is biased, we can say that;
- Yes, the sampling method is biased.
- The likely direction of the bias is because you only asked 5 people which
is not a significant percentage of those offering psychology majors and as
such the 4 out of 5 gotten is likely going to be an over estimation of those
who are willing to pay to join this club.
We are told that;
You want to start a club.This club is for psychology majors.You want to find the proportion of those in the psychology majors that will join this club you want to organize.Now, out of all the students offering psychology majors, you only asked 5 of them if they will be interested. Since 4 out of the 5 are interested and you want to use that to form a basis of the proportion of those interested , it would lead to sampling bias since the population is not adequately represented.Therefore, this would lead to sampling bias and thus the sample is biased.
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Use function notation to write the equation of the line
please asap
Answer:
The correct answer is the first option.
Step-by-step explanation:
The correct function notation is f ( x ) = x because the slope is 1, and the y-intercept is 0. The y-intercept is the point on the graph where it crosses the y-axis.
Therefore, the correct answer is the first option. Brainly isn't allowing me to post the equation for some reason.
Write an equation for the description
Tanmayi wants to raise $165 for a school fundraiser. She has raised $130 so far. How much more does she
need to reach her goal? Let m be how much more is needed.
Answer:
She needs $55 more dollars
Step-by-step explanation:
Answer:
[tex]m + 130 = 165 \\ m = 165 - 130 = 35 \: dollars[/tex]
How many groups of 3/4 are in 4 1/2
Answer:
5 1/2
Step-by-step explanation:
3/4+3/4+3/4+3/4+3/4+1/2= 4.25
4.25 = 4 1/2
The number of 3/4 groups is 6.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Total amount = 4(1/2) = 9/2
The number of groups.
= 9/2 ÷ 3/4
= 9/2 x 4/3
= 6
Thus,
There are 6 groups of 3/4.
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Jason, David, and Marcus each saved their allowance for four weeks. The ratio of total money
saved to number of weeks for each friend are shown in the table and graph. Which friend has
the greatest ratio of total money saved to number of weeks? Justify your response.
Answer:
David saved $15 per week
Jason saved $10 per week
Marcus saved $5 per week
(i divided y by x)
so David saved the most money throughout each week.
The price of a technology stock has risen to $9.66 today. Yesterday's price was $9.53. Find the percentage increase. Round your answer to the nearest tenth of a percent
Answer:
0.13
Step-by-step explanation:
PLEASE HELP ME ITS ALGEBRA THANK YOUUUU
Answer:
60
Step-by-step explanation:
24 ÷ 4 is 6. In 8 days He would have 48. Add two 6's and you get the number 60.
cual es la raíz cuadrada de 254
Answer: Es 15.9
Step-by-step explanation:
15.9373774505 ⬆️